We study the problem of electron-ion temperature equilibration in plasmas. We consider pure H at various densities and temperatures and Ar-doped H at temperatures high enough so that the Ar is fully ionized. Two theoretical approaches are used: classical molecular dynamics (MD) with statistical two-body potentials and a generalized Lenard-Balescu (GLB) theory capable of treating multicomponent weakly coupled plasmas. The GLB is used in two modes: (1) with the quantum dielectric response in the random-phase approximation (RPA) together with the pure Coulomb interaction and (2) with the classical (ℏ→0) dielectric response (both with and without local-field corrections) together with the statistical potentials. We find that the MD results are described very well by classical GLB including the statistical potentials and without local-field corrections (RPA only); worse agreement is found when static local-field effects are included, in contradiction to the classical pure-Coulomb case with like charges. The results of the various approaches are all in excellent agreement with pure-Coulomb quantum GLB when the temperature is high enough. In addition, we show that classical calculations with statistical potentials derived from the exact quantum two-body density matrix produce results in far better agreement with pure-Coulomb quantum GLB than classical calculations performed with older existing statistical potentials.